Lindner, Marko : An Identification of Convolution Operators on Cones

Author(s):

Lindner, Marko

Title:

An Identification of Convolution Operators on Cones

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 10, 2004

Mathematics Subject Classification:

47B35			[ Toeplitz operators, Hankel operators, Wiener-Hopf operators ]
47G10			[ Integral operators ]
47B38			[ Operators on function spaces ]

Abstract:

Simonenko studied properties of convolution type operators on cones in $\R^n$. The purpose of this note is to show that every convolution operator on a suitable cone in $\R^n$ or $\Z^n$ can be identified with a standard Wiener-Hopf operator, i.e. a convolution operator on $\R_+^n$ or $\Z_+^n$, respectively. We demonstrate this identification and give explicit formulae for the convolution kernels and symbols of these Wiener-Hopf operators.

Keywords:

convolution operator, Wiener-Hopf operator, Toeplitz operator, cone

Language:

English

Publication time:

7 / 2004